Simple Interest Vs. Compound Interest: A Beginner’s Guide

There are two types of interest that investments and savings vehicles can generate and that you can pay when borrowing money: simple and compound.

What’s the difference between simple interest and compound interest? It’s all about how the interest that you earn or pay is calculated.

It’s important to know which of your investments pays out simple interest and which generates compound interest because the second of those two options will generate more interest income over time. At the same time, you should know whether you’ll pay simple or compound interest when borrowing money. You’ll pay more over the life of your loan if you are paying compound interest.

What Is Simple Interest?

Simple interest is calculated solely on the original balance of your loan or investment. Say you invest $10,000 in a savings account that pays 3% interest each year. After 1 year, you'd earn $300 in interest: $10,000 x 0.03. You'd then have $10,300 in your account after 1 year, if you hadn't added any funds or made any withdrawals during this time.

What Is Compound Interest? 

Compound interest is more complicated. If you invest in a mutual fund, for example, that pays out in compound interest, you'll earn interest not only on the money you invested in the fund but on the interest that these dollars earn. Because of this, you'll earn more interest from savings vehicles that pay compound interest than you will by investing in those that only pay out simple interest.

Here's an example: Say you invest $10,000 in a certificate of deposit with a 5-year term that pays compound interest of 4% a year. During the first year, you'll earn the same amount of interest that you'd have earned if your CD earned simple interest: $400, or $10,000 x 0.04.

But starting in your CD's second year, you'd earn interest not only on your loan's principal balance, but on the interest that this CD has earned. You'd start year 2 of your CD with a balance of $10,400. In this year, you'd earn $416 in interest, or $10,400 x .0.04.

In year 5 of your CD, you'd earn $467.94 in interest, and your CD would have a total balance of $12,166.53, meaning that you would have earned a total of $2,166.53 in interest. If your CD had paid out simple interest during this time, you would have earned just $400 a year or $2,000 total, $166 less than you earned thanks to compound interest.

But what about when you’re borrowing money? Most auto loans and mortgage loans charge simple interest. However, if you carry a balance on your credit cards, you’ll pay compound interest, which is why your credit card debt can rise so quickly if you don’t pay it off in full each month.

Here’s an example: Say you have a balance of $8,000 on a credit card with an interest rate of 21%. If your minimum monthly payment is equal to 1% of your balance plus interest, it would come out to $220 a month. If you only paid that minimum payment each month and did not add to your card balance with spending, it would take you 326 months, or more than 27 years, to erase your debt and you'd pay $13,374.60 in interest, all thanks to compound interest.

The Difference Between Simple And Compound Interest

The difference between simple interest and compound interest is in how the interest on a loan, savings account or investment accrues. With simple interest, the interest you pay or earn only accrues on the original principal balance of your loan or investment amount. With compound interest, interest accrues on both the principal balance of a loan or investment and on the interest that you earn on this balance. 

How To Calculate Simple Interest 

To calculate how much you'll earn or pay in simple interest, you can rely on a basic formula:

Simple interest = Principal x Interest Rate x Time

In this formula, “principal” equals the initial balance, the amount that you either invested or borrowed. The “interest rate” is the interest rate that your investment vehicle earns or your loan charges. “Time” equals the number of years in which you'll earn interest or pay back your lender.

Here's an example of how paying simple interest works: Say you take out a personal loan of $20,000 with a 5-year term with an interest rate of 7% each year. You'd pay $7,000 in interest over the life of the loan, $20,000 x 0.07 x 5 years.

When you take out a student loan, mortgage loan, personal loan or car loan, you’ll generally be charged simple interest. Investments such as a certificate of deposit, money market account and savings account might also pay out in simple interest.

How To Calculate Compound Interest 

The compound interest formula is more complicated than the one used to calculate simple interest:

A = P(1 + r/n)^nt

In this formula, "A" equals the accrued amount that you'll earn or pay during the life of your loan or investment. "P" equals the principal amount that you invested or borrowed. The "r" equals the annual nominal interest rate as a decimal, while "n" equals the number of compounding periods each year. The "t" equals the time of your loan.

That’s a lot of math. Fortunately, many financial sites offer compound interest calculators that will do this math for you.

Say you invest $5,000 in a certificate of deposit with a term of 10 years and an interest rate of 8%. Say, too, that your interest is compounded once every year. After 10 years, your $5,000 will have grown to $10,794.50, a gain of more than $5,700.

A = P(1 + r/n)^nt

A = $5,000 (1+.08/1)^1*10

A = $5,000 (2.1589)

A = $10,794.50

You can earn even more if your interest compounds on a biannual basis, or two times a year. Say you invest the same $5,000 in a 10-year CD with the same interest rate. If your interest is compounded two times a year instead of once, you'll have earned $10,955.62 after 10 years, or more than $160 more. The formula to calculate this would look like:

A = $5,000 (1+.08/2)^2*10

A = $10,955.62

Compound interest is often applied with certificates of deposits, stocks, bonds, index funds, mutual funds and high-interest savings accounts.

Other Terms You Should Know

The world of interest comes with its own jargon. Here are some of the key terms you should know:

• Principal: The principal is the initial amount that you deposit in an investment or take out as a loan. For instance, if you take out a mortgage of $250,000, that $250,000 is your principal. If you deposit $10,000 in a high-yield savings account, that $10,000 is the principal. 
• Annual percentage rate (APR): A loan’s interest rate and annual percentage rate, known as its APR, are not the same thing. Your loan’s APR is its interest rate plus any fees that your lender charges. Because of this, your APR will be higher than your interest rate. Comparing APRs is a better way to determine which loan is more expensive. 
• The Rule of 72: The Rule of 72 is a formula that can help you calculate when the money you invest might double. The formula works like this: The number of years it takes for your investment to double is equal to 72 divided by your investment vehicle's annual interest rate or expected rate of return. Say you invest in a high-yield savings account with an interest rate of 5%. Divide 72 by 5 to get 14.4. This means that your investment should double after a little more than 14 years.
• Rate of return: The annual rate of return is the percentage change in value that the money you invest is expected to earn each year. Say you invest in a stock and you expect that stock's value will increase by 8% each year. Your expected annual rate of return is 8%. If you invest $1,000 in your stock you can expect that your investment will be worth $1,080 after a year, your original investment of $1,000 plus the $80 you earn on that investment.

The Bottom Line

Ready to tackle the world of investments and harness the power of earning interest? Or maybe you want to track the interest that you are paying on your credit cards and loans. If so, it’s time to download the Rocket Money^SM app to create a central location for all your accounts, including investments, loans and credit cards.